Machining efficiency comparison direction-parallel tool path with contour-parallel tool path

In molds and dies manufacturing, estimation of the machining time of tool paths is a pre-requisite for planning the machining processes and balancing them. The machining time is computed by dividing the distance of the tool path by its feed-rate. This theoretical machining time always underestimates the actual time, because it does not take into account the effects of the acceleration and deceleration of the CNC machines. This paper proposes a machining time model that considers the acceleration and deceleration of the CNC machines. Using the proposed model, we compare the machining efficiency of the tool paths currently employed in molds and dies manufacturing—three types of direction-parallel tool paths (one-way path, pure-zig-zag path, and smooth-zig-zag path) and contour-parallel tool path. The results of the comparison simulation reveal that the smooth-zig-zag path is the most efficient regardless of feed-rates and path intervals and that the effects of acceleration and deceleration are notably revealed at higher feed-rates.     

Linear and angular feedrate interpolation for planar implicit curves

In multi-axis CNC machining, a cutting tool combines translation and rotational movements with respect to a workpiece. This entails CNC interpolation to take angular feedrates defining the speed of the rotational movement into account, while current interpolations are overwhelmingly based on linear feedrates defining the speed of the translation movement. This paper considers linear and angular feedrate interpolations of 2D tool paths for multi-axis machining. A 2D tool path is identified by a position curve assumed to be a 2D implicit curve and a tool orientation curve based on the implicit curve. The paper will relate the angular feedrate to the linear feedrate along the tool paths. The result is then used to develop the angular feedrate interpolation from the linear feedrate interpolation. Detailed interpolation schemes for such hybrid feedrates as a constant linear feedrate with constrained angular feedrate (CLCA) and a constant angular feedrate with constrained linear feedrate (CACL) have further been constructed. A corrected interpolation scheme is further present to augment the initial interpolation. Example interpolations including a quadric curve, the nodal cubic and a quartic curve are carried out to illustrate the feasibility and effectiveness of the proposed approach.     

An effective approach for non-singular trajectory generation of a 5-DOF hybrid machining robot

By taking a newly developed 5-DOF (degree of freedom) hybrid robot as an exemplar, this paper presents a novel and effective approach for non-singular tool trajectory generation. Based upon singularity analysis via inverse kinematics, an algorithm for the C-axis path optimization is developed using the weighted S-curve. Incorporated singular domain detection with the C-axis angle correction, the algorithm can easily be programmed and embedded into the CNC (computer numerical control) system as a postprocessing module and works in real-time. Then, an offline feedrate scheduling method is proposed by considering the drive and geometric accuracy constraints, allowing the rapid yet smooth movement in the neighborhood of singularity to be achieved. Additionally, it is found that the orientation accuracy can be improved by setting adequate cone angle and feedrate value. The results of both simulations and experiments on a prototype machine show that the C-axis can follow the non-singular tool trajectory well with relatively high rotary speed to pass through the singular domain, thereby verifying the effectiveness of the proposed approach.     

Quart-parametric interpolations for intersecting paths

The intersecting path is an important tool path generation method. This paper proposes an approach for the quart-parametric interpolation of intersecting paths. The objective of our approach is that the intersecting paths for surface machining can be directly interpolated within the computer numerical control (CNC) system. This enables the CNC interpolator to process the intersecting paths without geometric approximation as in existing approaches and take into consideration any specific feedrate profiles and further machining dynamical issues along the path.The interpolation of the intersection of two general parametric surfaces is transferred into interpolation of its projection curves and the time trajectories of four parameters along the intersecting curves are obtained. Our strategy is to carry out the quart-parametric interpolation based on the projection interpolation. The feedrate control method is developed, and then the interpolation algorithms for two projection curves are proposed. An error reduction scheme is presented to alleviate point deviation from the drive parametric surface. Simulations of quart-parametric interpolation have been carried out to verify the effectiveness of the proposed algorithm.     

Smooth time-optimal tool trajectory generation for CNC manufacturing systems

An optimization approach is proposed in this paper for generating smooth and time-optimal path constrained tool trajectory for Cartesian computer numerical control (CNC) manufacturing systems. The desired smooth time-optimal trajectory generation (STOTG) problem is formulated as a general optimal control problem. And axis jerk (derivative of acceleration with respect to time) constraints are introduced into this problem to remove discontinuities of the acceleration profiles. The desired smoothness of the trajectory can be accomplished by adjusting the values of jerk constraints. A control vector parameterization (CVP) method is applied to convert the optimal control problem into a nonlinear programming (NLP) problem which can be solved conveniently and effectively. The third derivative of the path parameter with respect to time (pseudo-jerk) and jerk act as optimization variables. The pseudo-jerk is approximated as piecewise constant, thus for at least second-order continuous parametric path, the resulted optimized trajectory with respect to time is also at least second-order continuous. Sequential quadratic programming (SQP) method is used to solve the NLP problem, through which numerical solution is obtained. Non-smooth (i.e. without considering jerk constraints) time-optimal trajectory generation (non-STOTG) problem is also considered in this paper for the purpose of comparison. Solutions of time-optimal trajectory generation (TOTG) problems for two test paths are performed to verify the effectiveness of the proposed approach.     

A time-scaling method for near-time-optimal control of an omni-directional robot along specified paths

This paper proposes a time-scaling method to determine the near-time-optimal movement of an omnidirectional mobile robot along a given reference path. With this strategy, the positions of the trajectory after scaling are the same as the original ones such that the geometric path constraints are not violated. However, the velocities and the accelerations are adjusted to meet the dynamical constraints and to minimize the traveling time. When determining the time-scaling function, a cubic spline interpolation technique is used, in which control points for interpolation are determined simultaneously by a particle swarm optimization (PSO) method based on the integration of a time-scaling function. To show the feasibility of the proposed method, the results of a simulation example is illustrated. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

A novel cartesian trajectory planning method by using triple NURBS curves for industrial robots

This article presents a novel method of robot pose trajectory synchronization planning. First of all, based on triple NURBS curves, a method of describing the position and orientation synchronization of the robot is proposed. Then, through considering geometric and kinematic constraints, especially angular velocity constraint, and employing bidirectional interpolation algorithm, a robot pose trajectory planning approach is developed, which has limited linear jerk, continuous bounded angular velocity and approximate optimal time, and does not need an optimization program. Ultimately, two robot pose paths, blade-shaped curve and fan-shaped curve, are utilized for simulations, and the results indicate that the proposed trajectory planning method can satisfy the given constraint conditions, i.e. the linear jerk is limited and the angular velocity is continuous bounded. The trajectory tracking experiments are further carried out on a 6-DOF industrial robot, and the results show that the proposed planning method can generate smooth trajectories to ensure the stability of the robot motion without impact in practical situations.     

On the effective tool path planning algorithms for sculptured surface manufacture

This paper describes the cutter path planning and cutter interference (gouging) analysis algorithms developed to generate optimal tool path for manufacturing sculptured surfaces on three axes CNC machine tools. Cutter path planning algorithm approximates the parametric curves on three dimensional surfaces by a sequence of straight line segments and generates optimal tool paths by minimizing the number of interpolation points while keeping the path deviations within the specified tolerances. Cutter interference analysis algorithm checks for the self intersection of an offset surface and determines the self-intersection curve. The tool path is then planned over the cutter contact (CC) surface after removing the CC data that lies inside the self-intersection curve. Finally, the effectiveness of these algorithms is demonstrated by implementing them in CAD/CAM system.     

Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines

In CNC machining, fitting the polyline machining tool path with parametric curves can be used for smooth tool path generation and data compression. In this paper, an optimization problem is solved to find a quadratic B-spline curve whose Hausdorff distance to the given polyline tool path is within a given precision. Furthermore, adopting time parameter for the fitting curve, we combine the usual two stages of tool path generation and optimal velocity planning to derive a one-step solution for the CNC optimal interpolation problem of polyline tool paths. Compared with the traditional decoupled model of curve fitting and velocity planning, experimental results show that our method generates a smoother path with minimal machining time.     

Integrated sliding-mode algorithms in robot tracking applications

An integrated solution based on sliding mode ideas is proposed for robotic trajectory tracking. The proposal includes three sliding-mode algorithms for speed auto-regulation, path conditioning and redundancy resolution in order to fulfill velocity, workspace and C-space constraints, respectively. The proposed method only requires a few program lines and simplifies the robot user interface since it directly deals with the fulfillment of the constraints to find a feasible solution for the robot trajectory tracking in a short computation time. The proposed approach is evaluated in simulation on the freely accessible 6R robot model PUMA-560, for which the main features of the method are illustrated.     

A universal velocity limit curve generator considering abnormal tool path geometry for CNC machine tools

Non-linear parametric curves, such as B-spline curves, are becoming increasingly available in modern CNC (Computer Numerical Control) systems. The smoothness of parametric curves offers higher order of continuity and thus invokes less vibration in machines as compared to short line segments. Nevertheless, the computations for velocity limit curves, velocity profiles and interpolation points are quite complicated and time-consuming and therefore approximation methods are applied. Unnecessary accelerations and decelerations, which cost additional time of motion, can be caused by inaccurate computations of the velocity limits around tiny corners. To overcome the problem, the unit arc length increment scanning method (UALISM) is proposed to reduce the time of movement and to improve the efficiency. The scanning interval is fixed at 1 BLU (basic length unit) which is irrelevant to the type, size and shape of the tool path curve. The constraints of chord height errors and axis accelerations are considered and the velocity limit for the specified scanning point is computed using the coordinates of multiple scanning points near the specified scanning point. Simulation results show that the unnecessary accelerations and decelerations can be avoided and thus the total motion time can be reduced by UALISM.     

Continuity-preserving tool path generation for minimizing machining errors in five-axis CNC flank milling of ruled surfaces

Five-axis CNC flank machining has been commonly used in the industry for shaping complex geometries. Geometrical errors typically occur in five-axis flank finishing of non-developable surfaces using a cylindrical cutter. Most existing tool path planning methods adjust discrete cutter locations to reduce these errors. An excessive change in the cutter center or axis between consecutive cutter locations may deteriorate the machined surface quality. This study developed a tool path generation method for minimizing geometrical errors on finished surfaces while preserving high-order continuity in the cutter motion. A tool path is described using the moving trajectory of the cutter center and changes in two rotational angles in compact curve representations. An optimization scheme is proposed to search for optimal curve control points and the resulting tool path. A curve subdivision mechanism progressively increases the control points during the search process. Simulation results confirm that the proposed method not only enhances the computational efficiency of tool path generation but also improves the machined surface finish. This study provides a computational approach for precision tool path planning in five-axis CNC flank finishing of ruled surfaces.     

FPGA-based hardware CNC interpolator of Bezier,splines, B-splines and NURBS curves for industrial applications

Tool path interpolation is an important part of Computerized Numerical Control (CNC) systems because it is related to the machining accuracy, tool-motion smoothness and overall efficiency. The use of parametric curves to generate tool-motion trajectories on a workpiece for high accuracy machining has become a standard data format that is used for CAD/CAM (Computer Aided Design/Computer Aided Manufacturing) and CNC systems. Splines, Bezier, B-splines, and NURBS (Non-Uniform Rational B-splines) curves are the common parametric technique used for tool path design. However, the reported works bring out the high computational load required for this type of interpolation, and then at best only one interpolation algorithm is implemented. The contribution of this paper is the development of a hardware processing unit based on Field Programmable Gate Arrays (FPGA) for industrial CNC machines, which is capable of implementing the four main interpolation techniques. It allows the selection of the required interpolation technique according the application. Two CAD models are designed for test the CNC interpolations; experimental results show the efficiency of the proposed methodology.     

Software-based tool path evaluation for environmental sustainability

Currently available life cycle assessment (LCA) tools provide only a rough estimation of the environmental impact of different manufacturing operations (e.g. energy consumption). To address this limitation, a web-based and application programming interface (API) based process analysis software tools were developed to estimate the energy consumption of a computer numerically controlled (CNC) machine tool operation and to evaluate its environmental impact as a first step towards sustainable manufacturing analysis. Acceleration/deceleration of machine tool axes and the direction of axes movement were considered to estimate the total energy demand and processing time of the machine tool operation. Several tool path generation schemes were tested to analyze the energy consumption and resulting green house gas emission of CNC machine tool operation. It showed that tool path generation schemes affect the amount of energy and the processing time required to machine the same part, and location of the machining resulted in different amount and characteristics of green house gas emission.     

Automatic surface roughing with 3D machine vision and cooperative robot control

This paper presents an innovative and practical strategy for automated leather surface roughing, using structured light 3D machine vision for object profile perception, and NURBS interpolation for accurate and smooth trajectory generation. As high pressure grit blasting is used for roughing, considering the spacial constraints in the blasting chamber, an additional degree of freedom is introduced using a rotary table, which supports the workpiece. Cooperative control is implemented between a 6-DOF robot and the rotary table to minimize robot movements, while satisfying the requirements of variable velocity control, accurate trajectory tracking and orientation control. Experimental results of consistent roughing performance have shown the efficiency of the proposed method.     

参数曲线插补自适应加减速控制方法研究

CNC系统中参数曲线插补广泛地应用于复杂轨迹的生成.为了弥补参数曲线插补时加减速能力的不足,提出自适应的加减速控制方法.在插补预处理中,对轮廓误差引起的速度变化曲线进行分析,在加加速度满足要求的同时,对加速度的变化进行控制.应用该方法,在保证系统加工精度的基础上,可以根据曲线的形状,自适应的调整进给速度,使进给速度变化趋于平滑,有效地避免了加速度和加加速度的变化对伺服系统造成的机械冲击.文中给出了B样条曲线插补的实例对控制方法进行了说明和验证.仿真结果表明,该方法切实可行而且有效.     

Dynamic Modeling and Tracking Control of a Nonholonomic Wheeled Mobile Manipulator with Dual Arms

This paper presents methodologies for dynamic modeling and trajectory tracking of a nonholonomic wheeled mobile manipulator (WMM) with dual arms. The complete dynamic model of such a manipulator is easily established using the Lagrange’s equation and MATHEMATICA. The structural properties of the overall system along with its subsystems are also well investigated and then exploited in further controller synthesis. The derived model is shown valid by reducing it to agree well with the mobile platform model. In order to solve the path tracking control problem of the wheeled mobile manipulator, a novel kinematic control scheme is proposed to deal with the nonholonomic constraints. With the backstepping technique and the filtered-error method, the nonlinear tracking control laws for the mobile manipulator system are constructed based on the Lyapunov stability theory. The proposed control scheme not only achieves simultaneous trajectory and velocity tracking, but also compensates for the dynamic interactions caused by the motions of the mobile platform and the two onboard manipulators. Simulation results are performed to illustrate the efficacy of the proposed control strategy.     

Interpolation of orientation for precise path generation in industrial robots

Industrial robots are versatile mechanical systems that require accurate tracking of continuous end-effector trajectories. However, a variety of control problems are encountered due to the deviation between the desired and actual paths.In this study, a new continuous path planning method based on an interpolation of orientation scheme is applied for precise path generation in robot welding. This method guarantees minimum deviation of positioning and orientation errors. Also, a new trajectory error evaluation strategy is developed to describe the trajectory errors at the effect points, which are very important in some robot jobs such as arc-welding operations.The simulation study of circular motions in arc-welding operations shows the effectiveness of the proposed approach.     

数控加工中路径规划与速度插补综述

数控技术在现代制造工业中被广泛使用,相关研究一直为学界和业界共同关注。数控技术的传统流程主要包含刀具路径规划和进给速度插补。为实现高速高精加工,人们通常将路径规划与速度插补中的若干问题转换成数理优化模型,针对工程应用问题的复杂性,采用分步迭代优化的思路进行求解,但所得的结果往往只是局部最优解。其次,路径规划与速度插补都是为了加工一个工件曲面,分两步进行处理虽然简化了计算,但也导致不能进行整体优化。因此,为了更好地开展路径规划与速度插补一体化设计与全局最优求解的研究,系统性地了解并学习已有的代表性工作是十分有必要的。所以将逐次介绍数控加工中刀具路径规划与速度插补的相关方法与技术进展,包括基于端铣的加工路径规划;刀轴方向优化;G代码加工以及拐角过渡;参数曲线路径的进给速度规划等国内外相关研究以及最新提出的一些新型加工优化方法。     

基于四阶贝塞尔曲线的无人车可行轨迹规划

对于实际的无人车系统来说,轨迹规划需要保证其规划出来的轨迹满足运动学约束、 侧滑约束以及执行机构约束.为了生成满足无人车初始状态约束、目标状态约束的局部可行轨迹,本文提出了一种基于四阶贝塞尔曲线的轨迹规划方法.在该方法中, 轨迹规划问题首先被分解为轨形规划及速度规划两个子问题.为了满足运动学约束、 初始状态约束、目标状态约束以及曲率连续约束,本文采用由3个参数确定的四阶贝塞尔曲线来规划轨迹形状.为了保证转向机构可行,本文进一步采用优化方法求解一组最优参数从而规划出曲率变化最小的轨线.对于轨线执行速度规划,为了满足速度连续约束、加速度连续约束、加速度有界约束以及目标状态侧滑约束,本文首先求解了可行的轨迹执行耗时区间,再进一步在该区间中求解能够保证任意轨迹点满足侧滑约束的耗时,最后再由该耗时对任意点速度进行规划.本文结合实际无人车的应用对轨迹搜索空间生成、道路行车模拟以及路径跟踪进行了仿真实验,并基于实际的环境数据进行了轨迹规划实验.